This is a collection of classroom documents for the two courses I am teaching at international Master in Theoretical Physics and Applications :
Introduction to Dynamical Systems
Exercices:
Bibliography:
- Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics), by Stephen Wiggins – Springer
- Chaos: An Introduction to Dynamical Systems, by Kathleen T. Alligood, Tim D. Sauer, James A. Yorke – ISBN-13: 978-0387946771
- Chaos and nonlinear dynamics an introduction for scientists and engineers, by Robert Hilborn – ISBN-13: 978-0198507239
Quantum Information Theory
- Introduction :
- quantum information vs classical information ;
- quantum complexity ;
- physical implementation.
- Qu-bits and density matrices:
- definition,
- Bloch sphere,
- Gleason theorem.
- Entanglement:
- EPR pairs and hidden information,
- Bell inequalities.
- Application to the quantum teleportation
- Measurement:
- orthogonal measurement,
- POVM,
- complete positivity.
- Quantum algorithms:
- complexity classes
- Grover algorithm
- factoring
- Quantum error correcting codes:
- depolarizing channel
- CSS codes
- Some useful bounds
- Stabilizer codes.